Thermal Efficiency Calculator

How it works

1. 1For a real heat engine, enter the work output W (J) and heat input Qin (J): η = W ÷ Qin × 100, plus wasted heat (Qin − W).
2. 2For the Carnot method, enter the cold and hot reservoir temperatures in °C or °F (converted to kelvin): η = (1 − Tcold ÷ Thot) × 100.
3. 3Switch metric (°C) / imperial (°F) for the Carnot inputs; reservoir temperatures are shown in kelvin.

Use cases

• Students verifying heat-engine homework and seeing how much energy is lost as waste heat.
• Instructors demonstrating Carnot limits — a turbine between 100 °C and 500 °C maxes out near 52%.
• Engineers comparing a plant’s measured efficiency against the Carnot ceiling.

Frequently asked questions

What is the formula for thermal efficiency?

For a heat engine, η = W ÷ Qin × 100, where W is net work output and Qin is heat supplied (both in joules). An engine doing 400 J from 1000 J is 40% efficient; the other 600 J is rejected as waste heat.

What is Carnot efficiency and why does it matter?

It is the theoretical maximum between two reservoirs: η = (1 − Tcold ÷ Thot) × 100, with temperatures in kelvin. Tcold = 300 K and Thot = 600 K give 50%. No real engine can exceed this ceiling.

Why must temperatures be in kelvin for the Carnot formula?

It is derived from absolute thermodynamic temperature. Celsius or Fahrenheit, with arbitrary zero points, would give wrong ratios. The tool converts °C/°F to kelvin (0 °C = 273.15 K) before computing Tcold ÷ Thot.